I'm thinking this may be what's going on. OP, when you said you used a fine mesh strainer, where did you get it from? What's fine mesh to one might be coarse to another.
Mine looks like this:
View attachment 329068
I think it would be more or less similar to a cocktail strainer. It's really a double-mesh, a coarse mesh which supports the fine mesh.
When I transfer from the boil kettle to the fermenter I strain the wort through this strainer; it catches the vast majority of cold/hot break.
I don't do all-grain, but I'm sure it would catch most of what one would transfer.
and i got it from a store called marshalls/home goods.